Question

FORM ONE DECEMBER HOLIDAY ASSIGNMENT 2023. 1. The following measurements were recorded in a field book of a farm in metres (XY = 400m) C 60 B 100 A 120 iv. V. Y 340 300 240 220 140 80 X a) Using a scale of 1cm representing 4000 cm, draw an accurate map of the farm. (4mks) b) Calculate the area of the farm in hectares. 120 D 100 E 160 F (4mks) c) If the farm is on sale at Kshs.80,000.00 per hectare, find how much it costs. (2mks) 2. On a certain map, a road 20km long is represented by a line 4cm long. Calculate the area of a rectangular plot represented by dimensions 2.4cm by 1.5cm on this map - leaving your answer in hectares. 3. Three towns A B and C are situated such that town A is 40km from B on a bearing of 280°, C is 60km from B on a bearing of 130° Another town D is only 10km from C on a bearing of 210° (a) Drawing accurately and using a scale of 1cm to 10km show the relative positions of A, B, C and D (b) find the:- i. ii. Distance from A to C and the bearing of A from C Distance of B from D Distance of A from D Bearing of A from D Bearing of C from D 3mks. 4. Ayub travelled part of the journey by train and the rest of the journey by bus. The total fare was Ksh 4000. On return, the fare of the bus was hiked by a half of what he had paid and the total fare of the return journey hiked to Ksh 4800. Find the train fare(3mks) 5. When 19346 is divided by a number, the quotient is 841 and the remainder is 3. What is the number? (3mks). 6. A square toilet is covered by a number of whole rectangular tiles of sides 60cm by 48cm. Calculate the least possible area of the room in square metres. (3mks).​

Answer 1

To solve scale drawing and map representation problems, we use the given scale factor to convert real-life measurements into the scaled size. Multiplying the actual distances by the scale factor yields the scaled distances, which can then be represented on maps or models. Similarly, the area of drawings can be determined by converting dimensions to real-life measurements and calculating accordingly.

Step-by-step explanation:

Scale and Measurement in Mathematics
To solve problems involving scale drawings and map representations, we convert real-life measurements into a scale that fits on a map or a model. When the scale factor is given, such as 1/800 for the map in the question, and the actual distance is known (80 meters between Calvin's house and Frank's house), we can calculate the scaled distance by multiplying the actual distance by the scale factor. Since 1 cm on the map represents 80 m in real life, the distance on the map would be 80 m × (1 cm / 800 m) = 0.1 cm in centimeters.
For the second question, the distance from Calvin's house to the park would similarly be calculated: 40 m × (1 cm / 800 m) = 0.05 cm. If the distance to the corner store is twice that to Frank's house, then it would be 0.2 cm on the map. If the distance to his Grandmother's is halfway, the distance on the map would be 0.05 cm.
When given the scale for a meeting room drawing, such as 1 cm-2 m, and the drawing measurements are 1.5 cm by 2.5 cm, the area in real life can be calculated by first converting the drawing measurements to meters, then multiplying to get the area: (1.5 m × 2.5 m), which would be 3.75 m2 or 37500 cm2 because there are 10000 cm2 in a m2.

Lastly, if Samir ran a race that was 10 kilometers long, it means he ran 10,000 meters as there are 1,000 meters in a kilometer.